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- ItemAlgebraic K-theory and Motivic Cohomology(Zürich : EMS Publ. House, 2013) Huber-Klawitter, Annette; Jannsen, Uwe; Levine, MarcAlgebraic K-theory and motivic cohomology are strongly related tools providing a systematic way of producing invariants for algebraic or geometric structures. The definition and methods are taken from algebraic topology, but there have been particularly fruitful applications to problems of algebraic geometry, number theory or quadratic forms. 19 one-hour talks presented a wide range of latest results on the theory and its applications.
- ItemAnalytic Number Theory(Zürich : EMS Publ. House, 2013) Montgomery, Hugh L.; Vaughan, Robert C.; Wooley, Trevor D.Analytic number theory has florished over the past few years, and this workshop brought together world leaders and young talent to discuss developments in various branches of the subject.
- ItemAlgebraic Groups(Zürich : EMS Publ. House, 2013) Jantzen, Jens Carsten; Reichstein, ZinovyLinear algebraic groups is an active research area in contemporary mathematics. It has rich connections to algebraic geometry, representation theory, algebraic combinatorics, number theory, algebraic topology, and differential equations. The foundations of this theory were laid by A. Borel, C. Chevalley, T. A. Springer and J. Tits in the second half of the 20th century. The Oberwolfach workshops on algebraic groups, led by Springer and Tits, played an important role in this effort as a forum for researchers, meeting at approximately 3 year intervals since the 1960s. The present workshop continued this tradition, featuring a number of important recent developments in the subject.
- ItemMini-Workshop: The p-Laplacian Operator and Applications(Zürich : EMS Publ. House, 2013) Lindqvist, Peter; Kawohl, BerndThere has been a surge of interest in the $p$-Laplacian in many different contexts from game theory to mechanics and image processing. The workshop brought together experts from many different schools of thinking to exchange their knowledge and points of view.
- ItemMini-Workshop: The Willmore Functional and the Willmore Conjecture(Zürich : EMS Publ. House, 2013) Metzger, Jan; Neves, AndreThe Willmore functional evaluated on a surface immersed into Euclidean space is given by the $L^2$-norm of its mean curvature. The interest for studying this functional comes from various directions. First, it arises in applications from biology and physics, where it is used to model surface tension in the Helfrich model for bilipid layers, or in General Relativity where it appears in Hawking’s quasi-local mass. Second, the mathematical properties justify consideration of the Willmore functional in its own right. The Willmore functional is one of the most natural extrinsic curvature functionals for immersions. Its critical points solve a fourth order Euler-Lagrange equation, which has all minimal surfaces as solutions.
- ItemComputational Electromagnetism and Acoustics(Zürich : EMS Publ. House, 2013) Hoppe, Ronald H.W.; Joly, Patrick; Langer, UlrichComputational electromagnetics and acoustics revolve around a few key challenges, among which are the non-local nature of the underlying phenomena and resonance effects. The bulk of the contributions to the workshop addressed mathematical and numerical approaches meant to grapple with these two difficulties. Frequency domain integral equation methods continue to receive much attention, with a particular focus on (i) frequency robust matrix compression algorithms through so-called directional schemes or “butterfly algorithms”, and (ii) domain decomposition approaches. Time domain integral equation methods still enjoy rapid development and much progress was made in their numerical analysis. Of course, efficient and accurate absorbing boundary conditions remain a persistent topic and were covered in a few contributions. Resonance induced phenomena in a broad sense affect the analytical and numerical model for meta-materials, periodic structures, and micro-structured media. There is a lot left to be explored in this field in terms of analysis and algorithm development and a few presentations were devoted to such issues.
- ItemClassical and Quantum Mechanical Models of Many-Particle Systems(Zürich : EMS Publ. House, 2013) Carlen, Eric; Desvillettes, LaurentThis meeting was focused on recent results on the mathematical analysis of many-particle systems, both classical and quantum-mechanical in scaling regimes such that the methods of kinetic theory can be expected to apply. Thus, the Boltzmann equation is in many ways the central equation investigated in much of the research presented and discussed at this meeting, but the range of topics naturally extended from this center to include other non-linear partial differential and integro-differential equations, especially macroscopic/fluid-dynamical limits of kinetic equations modeling the dynamics of many-particle systems. A significant subset of the talks focused on propagation of chaos, and the validation and derivation of kinetic equations from underlying stochastic particle models in which there has been much progress and activity. Models were discussed with applications not only in physics, but also engineering, and mathematical biology. While there were a number of new participants, especially younger researchers, an interesting aspect of the conference was the number of talks presenting progress that had its origins in the previous meeting in this series held in 2010.
- ItemC*-Algebren(Zürich : EMS Publ. House, 2013) Rordam, Mikael; Vaes, Stefaan; Voiculescu, Dan-VirgilC*-algebras play an important role in many modern areas of mathematics, like Noncommutative Geometry and Topology, Dynamical Systems, Harmonic Analysis and others. The conference “C*-algebras” brings together leading experts from those areas in order to strengthen the cooperation and to keep the researchers informed about major developments in the field.
- ItemMini-Workshop: Spherical Varieties and Automorphic Representations(Zürich : EMS Publ. House, 2013) Sakellaridis, YiannisThis workshop brought together, for the first time, experts on spherical varieties and experts on automorphic forms, in order to discuss subjects of common interest between the two fields. Spherical varieties have a very rich and deep structure, which leads one to attach certain root systems and, eventually, a “Langlands dual” group to them. This turns out to be important for automorphic forms, as it provides a (mostly conjectural) way to analyze periods of automorphic forms and related problems in local harmonic analysis.
- ItemDynamische Systeme(Zürich : EMS Publ. House, 2013) Hofer, Helmut W.; Yoccoz, Jean-ChristopheThis workshop continued the biannual series at Oberwolfach on Dynamical Systems that started as the “Moser-Zehnder meeting” in 1981. The main themes of the workshop are the new results and developments in the area of dynamical systems, in particular in Hamiltonian systems and symplectic geometry related to Hamiltonian dynamics. Highlights were the solution of a fifty year old problem in Arnold diffusion and a KAM-result on quasi-linear perturbations of the KdV-equation.